physics
posted by howard .
Three forces act on a moving object. One force has a magnitude of 83.4 N and is directed due north. Another has a magnitude of 47.2 N and is directed due west. What must be (a) the magnitude and (b) the direction of the third force, such that the object continues to move with a constant velocity? Express your answer as a positive angle south of east.

if the object moves with constant velocity, there must be no acceleration, hence no net force.
If the two known forces are u and v, we need w = (u+v) so that u+v+w = 0.
So, convert to rectangular components, add them up, and take the negative sum for the 3rd force. 
F1+F2+F3 = M*a = M*0 = 0.
83.4i  47.2 + F3 = 0.
F3 = 47.2  83.4i = 95.83 N.[60.5o] S. of E.